Geometrical determination of dip and strike of cored strata



1 Feb. '7, 1%@ P. suBKow 294969422 GEOMETRICAL DETERMINATION OF DIP ANDSTRIKE 0F CORED STRATA Filed May 3, 1943 7 Sheets-Sheet l INVENTOR.

Feb. 7, 1950 P. SUBKOW 2,496,422

I GEOMETRICAL DETERMINATION OF DIP AND STRIKE OF CORED STRATA Filed May3, 1943 7 Sheets-Sheet 2 INVENTOR.

Feb. 7 195@ P. SUBKOW GEOMETRICAL DETERMINATION OF DIP AND STRIKE OFCORED STRATA '7 Sheets-Sheet 5 Filed May 5, 1945 flip 38.5 3835235INVENTOR.

Feb. 7, 1950 P. SUBKOW GEOMETRICAL DETERMINATION OF DIP AND STRIKE OFCORED STRATA '7 Sheets-Sheet 4 Filed May 3, 1943 INVENTOR.

Feb. 7 119% P. SUBKOW 294969422 GEOMETRICAL DETERMINATION OF DIP ANDSTRIKE OF CORED STRATA Filed May 3, 1943 7 Sheets-Sheet 5 & E Q & w n gi Q Q Q Q w W N w va 9 V INVENTOR.

Feb Z, 1950 P. SUBKOW 294969422 GEOMETRICAL DETERMINATION OF DIP ANDSTRIKE OF CORED STRATA Filed May 3, 1945 7 Sheets-Sheet 6 BNVENTOR.

P. SUBKOW GEOMETRICAL DETERMINATION OF DIP AND STRIKE OF CORED STRATAFeb 5 @5639 7 Sheets-Sheet '7 Filed May 3, 1943 dygyo ayuy INVENTOR.

Patented Feb. 7, 195

UNITED STATE GEOMETRICAL DETERMINATION OF DIP AND STRIKE OF CORE-DSTRATA Philip Subkow, Los Angeles, Calif.

Application May 3, 1943, Serial No. 485,540

12 Claims. 1

This invention relates to core more particularly to a methodand-apparatus for the determination of the direction of strike ofstratum, or direction of dip and. angle of dip of stratum traversed byan earth bore hole. The importance of such information is now generallyrecognized by geologists, petroleum engineers, and mining engineers.

This case will be better understood by reference to the followingfigures taken together with the description of the invention.

In the drawings:

Fig. l is a diagrammatic illustration of the principles of thisinvention;

Fig. 2 is a vertical elevation of the apparatus employed in thisinvention;

Fig. 3 is a plan view of the apparatus;

Fig. 4 is a fragmentary side elevation showin the mounting of thecylinder;

Fig. 5 is a fragmentary side elevation showing the mounting of theplane; and

orientation, and i l the strata with respect to the core axis. I canalso determine this angle by grinding the core to a perfect cylinder andmeasuring the distance between the high and low point of the ellipse.This distance divided by the diameter of the cylinder is the tangent ofthe angle of apparent dip. I shall call this angle the apparent angle ofstratum dip of the core.

The angular and azimuthal deviation of the core when it was taken isthen determined by a taking a. survey reading of the bore hole at theFigs. 6 to 10 are charts showing the applicapoint Where the core hasbeen removed. various methods are now commonly employed for thispurpose, as will be well understood by those in the art.

In my method I take two or more cores from the same or closely adjacentstrata or from strata known to be substantially parallel at the pointsat which the cores are taken. It is desirable to obtain such cores whichare not identical in their of such cores as differently deviated.

may be visually observed, but if the strata are not 1 visible tov theunaided naked eye, the strata may usually be discovered by viewing thecore under ultra-violet light passing from a source, such as aquartzmercury lamp, the light from which has been filtered through a suitablefilter which will exclude a major portion of the visible spectrumportion of the light and transmit the deep violet and ultra-violet endof the spectrum. 'The core will be found to fiuoresce at the otherwiseinvisible surfaces of contact between strata, clearly showing up thestrata lines. The thus observed strata may then be traced with pencil,chalk, or other suitable means and their positions thus permamentlymarked on the core. The thus observed strata usually form an ellipsewhere their planes intersect the cylindrical surface of the core,unless, of course, as rarely occurs, the core has been taken so that itsvertical axis is perpendicular to the plane of the stratum. When thecore has been marked in the manner hereinbefore described so as todelineate the stratum, the angle that its plane makes with the axis ofthe core is determined in the conventional manner. This determination ofthe stratum angle may be conveniently accomplished, for example, byreflecting the core in a mirror and laying on! I shall speak Thus, ifthe azimuthal deviations of the bore at the points where the cores aretaken are the same, I desire that the inclinations of the bore at thosepoints be different; or if the inclinations are the same, I prefer thatthe azimuthal deviations be different. Also, both the inclination andazimuthal deviations may be different. These cores preferably may beobtained from the same bore hole or, if unobtainable from the same borehole, from a plurality of bore holes suificiently close together to bedrilled through the same or substantially parallel strata in a commonformation. If they are taken from the same bore hole, it will be foundthat the normal drilling operations will usually produce cores which aresufficiently differently deviated for my purposes. Frequently, moreover,bore holes are deliberately deviated by means of directional drilling,in which case substantial difierences in deviation between cores takenfrom adjacent strata may be produced. Cores obtained undersuchconditions are particularly applicable in the process of myinvention.

The principle of my method will now be more fully understood byreference to Fig. l, which angular or azimuthal deviation.

diagrammatically illustrates the relative positions of the cores inspace under the conditions for ascertaining the true dip of the stratum.I first establish the co-ordinate system NOWA, where A is a verticalline to the horizontal plane NOW, which is in turn parallel to thehorizontal surface of the earth. N represents north, W represents west.A is the point of intersection of the axes I and 2' of cores I and 2.Let core I and core 2 be two given cores taken from the same or fromparallel strata. The angle of dip of the stratum with respect to core I(i. e.,

the apparent dip of the stratum with respect to "azimuthal orientationof each of the axes of two core I) is given by the angle which the lineAC" makes with a plane perpendicular to the axes l:-. The angle of dipof the stratum makes an angle 90-b with respect to a plane perpendicularto the axis 2 of core 2. The axis I of core I has an azimuthal directionshown by angle a. The inclination from the vertical of the core axis Icorresponding to the bore hole at the point at Which the core is takenis shown by vertical angle e. The position of the core is thus fixed inspace except that its angular orientation around its axis I' as a centerof rotation is not yet determined. In other Words, the core may take aninfinite number of positions, as shown, by rotating core I around itsfixed axis I. Core 2, the secofid core which has been taken, has itsaxis directed in the direction shown by angle a. The inclination of itsaxis fronithe vertical is shown by the vertical angle f. The position orcore 2, then, is similarly fixed in space except for its angularorientation around its axis 2. In order to iix completely the positionsof the cores in space, a third criterion must be satisfied, that is,that the planes of the strata in core I and in core 2 be parallel, asthey necessarily were in the earth formation from which they were taken.In other words, for convenience of illustration in Fig. 1, the strata ofcores I and 2 must'lie iii parallel planes and in order to accomplishthis, cores I and 1 must be rotated 'arou'nd their axes I "and Z'fu'ntila common stratum plane is established. when this is done, theorientations or the cores are established and the direction aridinclination of the line of inclination of the stratum 'planeline A-D maythen be readily determined.

This may be done by establishing a verticalplane DAO passing through theline of maximum in'- clination of the common stratum plane. The line DOat the intersection of the said. vertical plane DAO with the horizontalplane DOW in dicates the azimuthal direction 0 or this me of maximuminclination, i. e., dip of the stratum. This me my be established bylaying on the plane of the stratum, and itsdip determined both indirection and amount, thus established. Briefly, may thus fix theseparameters of the strata as hereinbeiore described by first'estab}lishing the inclination of the strata with respect 'to the vertical axisof each oi two or more differ- "elitl'y deviated cores takenfl'bmeaid'stlata or adjacent strata and then establishing the verticalinclination and the azimuthal direction of the cores. Finally, I mayestablish the pesicion er the common or parallel strata planes in thecores by rotating the cores about their axes until the planes of thestrata in the cores are parallel to each other. All of the originalgeometrical parameters of the cores are then re-established in space asthey were in the earth, and I then can measure the actual direction andangle of dip of the parallel strata planes by establishing the directionof the line of maximum inclination of the strata which will always beperpendicular to the strike.

Conversely, I may establish the inclination and or morediiferentlydeviated cores by determining the true dip, both in angle of dip anddirection of dip. This I may do by the methods hereiii described or byemploying any other method, such as magnetic orientation, or byemploying electrical coring, or by ordinary geological methods' I willthen have established the line AD both in its azimuthal orientation,angle 0, and angle of dip, to wit, the angle 41. I then determine theazimuthal orientation and angular deviation or core I, and thus fix theaxis or said core in space at said orientation. I also fix the plane ofthe core/stratum so that its known line of maximum inclination is in thedirection or dip and at the angle of dip. This I do by rotating the coreI around its axis I until this is accomplished. I then find thedirection and inclination of the axis 2', which is necessary to placeits core stratum A in the plane of the core stratum of core I. This isthe desired position of the axis of core 2, both in inclination andazimuthal orientation. I may thus establish the direction andinclination of the axes I and 1' of cores I and 2 required for theparallelism of their strata or that necessary to'make the plane A inboth core I and core 2 identical. In this manner, having determined'the'angle and direction of dip of a stratum, I can determine theazimuthal direction and deviation of cores taken from the sameor'paran'e'i-stmte without surveyin'g-th'e bore hole.

'While in the application the method is generally characterized byreference to the cores and their manipulation, it is not necessary toemploy the cores thinselves in operating 'my method, although they maybeso used. The cores may be emulated by mounting a plane which willsimulate the stratum or the core such that the dip of the plane to theearth is equal to the apparent dip of the core stratum when the axis ofthe core is vertical. The angle which the line of maxirnumdipof the corestratum makes with the plane of the earth will be termed the apparentdip'fof the core stratum. I shall call such a plane the simulated" corestratum. The axis of the core is then the line dropped from the planeperpendicul'a'r to the "plane 'of the earth. '1 shall can this line thesimulated core axis. The plane may be positioned so that the'simulatedcore axis is inclined and directed as is the core or the bore hole atthepoint-at which it is taken in the earth. .I shall call theinclination and direction the simulated deviation" of the coreaxis. Asthe simulated core stratum is rotated around the simulatedc'ore axis,the plane will take various inclinations and directions. In each suchposition, the line in theplahe which is parallel to the earth 'is thesimulated strike" of the simulated nore'stra-tum, an'd'a line in theplane perpendicular to the simulates 's'tr'ike when the line is directeddown-dip is the simulated 'dip, and its is laeimenen-meme-horizontallane of the earth and its bearing is the angle of simulated dip and thedirection of simulated dip.

In carrying out this method, it is sometime I diflicult to locate thepositions of parallelism of the several planes, and a considerablenumber of settings must be made until, by trial and error,

the region of parallelism is determined.

This difliculty may be avoided by employing the following method. Theangle and direction of dip of the plane of the core stratum, when the isthe angle of dip. The same procedure is fol-1 A second curve is drawn.The point of tangency of the two curves lowed for the second core.

will be the position where the direction and angle of dip of the planesare equal, i. e., where the planes are parallel. Instead of using thecores themselves, I may use the simulated cores by establishing thedirection and angle of dip 'of the simulated core strata of twodifferently deviated cores and determine the position of parallelism asthe point of tangency of the curves, relating the angle of simulated dipto the direction of simulated dip of the simulated core stratum. In thismethod it is not necessary to employ two planes simultaneously, that is,each core, or the simulated core, may be traversed independently and itscurve drawn. The point of tangency of the two curves gives the directionand angle of the dip of the core stratum when the curves are parallel inspace. This is the direction and angle of dip of the core stratum inwhich the core is taken.

The method also includes the determination of the angle which theapparent dip makes with the plane of the earth and the direction oftheline of apparent clip for various positions of the simulated dip of thecore stratum. I may then draw curves relating the direction of apparentdip to the direction of simulated dip and a curve relating the directionof apparent dip to the angle of apparent dip. Two cases must bedistinguished. In one case the lines of apparent dip, when positioned inthe plane of the stratum from which the core is taken, are sensiblyparallel. This may occur, for example, when the axes of the cores aresimilarly directed but differently inclined, or when one of:

the cores is taken vertically and the axis of the other core is in thedirection of the dip of the stratum which is cored, or is 180 in theother direction.

The other case is when the cores diifer in inclination and directionsubstantially, i. e., the lines of apparent dip are not parallel whenpositioned in the plane of the stratum from which the core is taken.

In the first case, the lines of apparent dip are parallel in space whenthe core strata of the two cores are oriented in the direction andinclination simulating that of the strata from which the cores are takenand the inclination of the lines of apparent dip to the earth plane willbe equal.

Therefore, in the first case, the region of tangency of the curves ofthe simulated dip and the parallelism of the planes and therefore thedirection and angle of simulated dip, may be confirmed by the curvesrelating the direction to the inclination of the apparent dip and thedirection of simulated dip to the directionof simulated dip. In suchcase thedirection of each of the. lines of apparent dip should be thesame and the 1 difference in inclination of the lines of apparent dip tothe earths plane should be equal to the. difference inthe verticaldeviation of the cores.

"In the second case I employ thetheorem ofv descriptive geometry whichdefines the dip and strike-of a stratum when the direction andinclination of two non-parallel lines in the stratum are known. Thistheorem is described in Engi-.

so. determined by this theorem of descriptive geometry confirms thedirection and inclination ofdip as determined by the methods herein de-.scribed, thedetermination of dip is thus con-- firmed. -.Z

.- A convenient apparatus to-be used in any method for determining thestrike, dip, and direction of dip is illustrated in Fig. 2., In Fig. 2,la. is the base of the apparatus mounted on adjusting legs, 2a so thatthe base may be levelled (i. e., made parallelto the plane of theearth); 3 is a polar coordinate graph in the center of which isrotatably mounted a disc 4 upon a spindle 5. Permanently mounted uponsaid disc is a bearing bracket 6 in which is positioned a cylinder I infrictional engagement therewith, so mounted that cylinder I may berotated within the bearing bracket 6. On said bearing bracket ispositioned a scribe mark 8 in the plane bisecting the cylin-v of thehole is vertical (1. e., perpendicular to the bearing is an arm II, thearm therefore being at,

to the axis of the spindle. Upon this arm is mounted a protractor I8.The base of the protractor is parallel to the arm II. A plane I9 ishingedly mounted on spindle 20 and held in ad-' justment by set screwIS. The spindle 20 is per-.

pendicular to the axis of arm- I! and side Na and perpendicular to theprotractor I8 and the axis of spindle 20 passes through the center ofthe protractor I8. The arm I9a which is an extension of the plane I9carries a scribe mark I8 on the end of arm I911. The scribe mark is inline with the axis of the rod 20. The end of the plane I9 is madecircular to permit the passage of the arm 24, as the rod 22is rotated,to different positions, as will be described below.

Swivelly mounted by means of bolt 2| and nut 2I on the plane I9 is a rod22 carrying a level 23 so mounted as to be rotatably adjustable upon therod. The rod carries an arm 24 so mounted that the line .24 on arm 24 isparallel to the plane Since I have deter- Through the hole in cy1in- 7lla'ndf penpendicularrmthesaaziszof mat 22;. rod carries aaprotractor:25lwhi'chmay be: rotated. around a: bolt 25s andiheld .atany.desired=psitiom by meansot asetl'screw 21-; The: belt ill-passes?through the center. of: protractor: 255 andathe-line'.

through-the center of: protractor 33* andithroughz.

line'f Abubblefi is mounted on protractor:

To adjust. theinstrument, set the" scribeamarkt IO' at'the zero mark ofprotractor-B set the plane Iss0 that the scribe mark I8 is opposite'the:0.-

mari on protractor' W; set-therprotractor 25 so:-

that the zero is opposite the line: 24.; set. the hinge vertical andsetfi-theprotractor 33 at the zeroposition opposite the line 30" adjustthe-legs- 2a until the bubbles 28, 3B, and- 23 are inithtacentralposition; and' rotate the arm II;- The bubbles should b'e-in the centralposition at all,

positions of thearm l-TL Proper adjustments may be made by means of theadjusting screws: To;

The procedure forcarrying 'outmy methodmay behest described by:reference to particular. ex ampies.

EXAMPLE. 1-

This example illustrates a case-where'- the" d1"- rections oftheapparent dip'of the cores are parallel andin this case parallel tothe dip-of the strata" fromwhich" they are taken. Thisexample-shows alsothe application of the method; to vertical cores:

Core- I wastaken at"1'0;595"-feet; The: Bore holeat this depthhad avertical" inclination of 11%? and it was-directedsi 33WZTheapparent'dipof'- thecore stratum was measured as 51 After" leveliingthe'instrument as previously described; thepiane l9 with-th'e-markIU"Was=set at El en; the=protractor l8 and" locked in-placeby setscrew19". The cylinder Twas rotated" so thatthe'scribe mark- I D wasoppositel on protractor 9. The di'sc 4 was rotated-'until'thescribe=mark 8 was at' theposition S. 33*"Wi, taking-north'arbitrarilyasshown in- Fig. 3. I1 is now directed arb'l trarily toanyposition: 'I-'he set screw I3 is tightenedi The rodM'is rotated until'the bubbi'e 23show-s-that the arm is level; that is, paral lei to thebase l and-the plane of the-earth; The direction of the line-14 and arm"Mi is read by projecting the axis-of the rod 22 onto the co"-- ordinate:chartr 3 and" reading the directionof the arm andliner down-dip-omplanell 'asz thedirection. of a line directeddown-dip andI-L perpendicular tothe;said 'projectionl A convenient: devices fiarmak-ihgzthe projectionan'dLreadingIthe directionzof the perpendicular aibasehavingztwo'verticaluprights which=may be set againstitherendslof 'therodfiZZ; The edgeof the base. which sits: on la isv thus parallel to.the rod- 2 2. Set. a: right. triangle: against the. parallel edge; of:the; base: and readi the; angl'ez that. thisz perpendicularmakesiwithlthedirection north' or: any. other direction on: chart; 3.This gives: the direction I of .thesimulated dip; of. thesplane of; thesimulatedrcore stratum:

Set the protractor 25. smthat thefibubbleisdevel 8. ZIL. This: gives.the-anglethat. thesimulated" dip makes with the planeof thmearth; Setthe hinge Masonthatitiszverticai; This may be done convenientlybysetting; it against a straight edge on" airbase. so :th-atxit.ispenpendicular to. base l-. theprotractor 3'3 l1nti1bubb1ef35 is level.Read the angle oniprotractor 33 opposite theline 30-. gives theanglethat the apparent'dip makes withithe? plane of the earth when the;simulatedcore stratum: is positioned so :that the simulated:

dip: is: in: the: direction as determined above. Measure: thedirectionof the apparent dip; again readingrdown-dip ofJthe-plane 19. This may bedone aswbefore bynprojectingthe line 30 and-arm.

30 onto the. base; I and: reading. the direction. ldolwne-dinbymeasuring: the angle: made {by this. projection withxa direction suchasnorth; Re neat. this procedure for. several positions spaced;throughout 360; Such readings willbe hereinafter.termeda.traverse.

The following Table 1 gives the readings of. thedirectionof;dip,.angleof dip, and the corresponding: direction of apparent dip,and the angle: ofzalpparentldip in making the traverse for core l.v

Fig. 6 charts this data. On this figure the abscissa givesthe hearingof. the dip and' the apparent dip, depending upon' whether we arereading'curve'A' or'curveB or curve C'. Curve A charts thexbearing ofthesimulated dip which is read on the abscissa and the angle'ofthesimulated dip read on the ordinate. Curve 3' charts thehearingoftheapparent dip; which bearing is readon the'azbs'cissa againstthe angle of apparent dip which'is read on the ordinate; Curve C chartsthe bearing of the'apparent dip which is read on the ordinate againstthe corresponding hearing of thesimulated dip which is read on' theabscissa;

A second core was-taken at a depth of 10,561 feet in the same well.Itwasa vertical core and the angle of apparent clip was measured on thecore*as-'395. Whemthis' core is-traversed the cylinder 1 is rotated sothat the scribe mark in is opposite the zero on the protractor 9; Thespindle H- is then vertical; inwhich case, of course, the position ofthe-scribe mark Bis immaterial; The-protractorfi -islset at an angle of395: A- traversa made :as previously descrtbed. in regard to core-lwill'show the'direction of simulated dip for all positionsof'thewplaneis the same as the direction of the apparent dip and theangleof" dip of'the simulated core stratum rep-- resented -by theprotraoton 9 is equal to the angle of! apparent dip; and" that theseangles are equal tothe'original'apparent dip; te -wit; 39 .5 This may bepredicted without such traverse. A straight liner E; therefore, drawnon; the-chart; Fig; 6-, at 39.6 will. represent the. angle. of. the

andlreadithe angleprotractorafiropposite the line simulated dip' .foraiibea1'inss of. the simulated dip, and the straight a bearing of'S. 25W. That is to say, when the simulated core strata of cores I and '2 areboth 1directed so that the bearings of the simulated dips are each S. 25W., the bearings of-the line of apparent dip of each core strata willalso be .S. 25 W.

Referring to angle of dip of the simulated core stratum of core I is at395 when the dip is S. 25 W. It will also be seen by reference to curveB that the angle of the apparent dip of core I is 39.5". 'At, thisiposition of the simulated core stratum the direction of the dip and itsinclination ofeach plane are the same (i. e., the simulated core strataare parallel). At all other positions the angles-of dip are different(i. e., the planes are not parallel) It will also be seen that thebearing of the apparent dip of core I is S. 25. W., which is the same asthe (bearing of the dip. It therefore appears that the line of apparentdip is coincident with the simulated dip of theplane in this position ofthe apparent dip and the simulated dip. It will also be seen that thedirection :of the bearing of apparent dip is substantially the same asthe direction of the axis ofthe core. In other words, the line ofapparent dip when positioned in the plane whose dip is 395, S. 25 W. issubstantially sensibly in the same plane as the axis of the core. Itwill be observed that the sum of the angle of the dip, that is. 39.50",and the inclination of the axis, 11.75", is equal to 51.25,.

which is sensibly that of the apparent dip, 51. This further confirmsthe iact that the direction of the apparent dip and the direction of thesimulated dip and the direction of the axis of the core are thesame.

curve A, it will Ibe seen that the ..'I 'his core wastraversed aspreviously described. The angle of 255 was set upon the protractor -18and the scribe mark 8 was set at N. 67 E., and the scribe mark ID wasset opposite 14. Table 2 records the bearing of the simulated dip,corresponding angle of dip, corresponding hearing of apparent dip, andcorresponding angle of apparent dip.

Table 2 Angle Bearing of Angle of Bearing of Dip of Apparent ApparentDip Dip Dip Degrees Degrees .65 S. 39 E l 21 14 S. 86 E 12 11 N. 7 E- 1012 N. 62.5 E 10. 5 16. 5 N. 36 E. 13 26. 5 N. l.5 W: 20. 5 33 N. 35.5 W27. 5 39 N. 77 W.. 37. 5 S. 71 W- 39 38 S. 26 W.. 36 35. 5 S. 10 E 30 InFig. 7 I have charted (see curve G) the bearing of the simulated dipread upon the abscissa against the angle of dip read on the ordinate. Oncurve H, I have charted the bearing of the apparent dip against theangle of apparent dip.

In Fig. 8 (curve I) I have charted the bearing of the dip read on theabscissa against the hearing of the apparent dip read on the ordinate.

Core 4 was taken from the same well at a depth of 4520 feet. The borewas directed at this point N. 68 E. and had a vertical inclination of17. The apparent dip of the core stratum was read as 21. This core wastraversed as previously described by setting 21 on the protractor Thesecurves therefore show that core I was taken so that its axis wassensibly in the direction of the dip and that the direction of the dipwas S. 25 W. with an inclination of 39.5. At this point only are thesimulated planes of cores l and 2 parallel, to wit, they have the samedirection of dip and the same angle of dip. This in this position willwe find that the direction of the apparent dip of the core strata ofeach of the cores I and 2 when positioned in the strata" from which theyare taken and the direction 0 the dip of the strata are the same.

EXAMPLE 2.

In the following example. cores were taken in similarly directedpositions but differently inclined, neither of the cores being;vertical. The

, direction of the apparent dips are the same but of differentinclinations to the coreaxis. In this {8, setting the scribe mark 8 atN. 68 E. and the scribe mark 10 opposite 17 on protractor .9. Table 3gives the bearing of the dip and the corresponding angle of dip, thecorresponding bearing of apparent dip, andthe corresponding angle atapparent clip. I

Table 3 Angle Bearing of Angle of I 1 Bearing of Dip of ApparentApparent Dip 1p Dip Degrees Degrees S. 3 W 20.5 S. 55.5 E. 11.5 7 N.88.5 E 4 4 N. 71 E... 3 5 6; Mt it 2 5 23 N. 1 W... 14% W 37 N. 66 W.-34% S. 67 W 38 S. 64 W-. 37 S. fil /2 W.. 37 S. 31 W-. 34 S. 28% W 31%S. 11 E 24% case, since the lines ofapparent-dip are in the of 14 and adirection of N. 67 E. The apparent dip of the core stratum was measuredas .2 5j.5.

I These data are plotted on Fig. 7 (curve J) giving thebearing ofthe-dip read upon the abscissa against the angle of dip read on theordinate. .CurveK gives the bearing of the apparent dip ,read on theabscissa against the angle of apparent dip read on the ordinate. Curve L(Fig. 8). gives the bearing of the apparent dip read on ordinate againstthe bearing of simulated dip read on the abscissa.

It will be observed that curves G and J, while not tangent, approacheach other in the region of about S.- W. to S. 80 W., being separatedcross in the region of about S. W. The crossv to be explained as arisingfrom a small inaccuracy dip is 24.75".

' the new setting of 24.75". bearing of dip, corresponding angle of dip,the

ing of the curves of I and L indicates that when "the bearing of the dipof both planes of cores 3- and 4 are S. 65 W., the bearings of theapparent dip of both cores are likewise S. 65'W.

In other words, in this position of each of the j core strata, thebearings of the apparent dips of both planes are the same and are equalto the bearings of the dip of each plane, i. e., the simulated corestrata, and dthcir apparent dips are coincident or parallel. In view ofthe sensibly identical direction of the core axes of cores 3 and 4-,this identity of the bearings. of the.- apparent dips is to be expected.

The separation of curves G and J is therefore in the reading of theapparent dip of the planes. If the apparent dip of core 3 is 24.75 andthe ap parent dip of core 4 is 21.75, these curves G and J approach eachother and become tangent. Table 2a gives the readings of the bearing ofdip and the corresponding angle of dip. the

bearing of apparent dip, and the angle of apparent dip on the assumptionthat the apparent Table 2-a Angle Bearing of Angle of Hearing Dip ofApparent Apparent Dip Dip Dip:

Degrees Curve G is the curve corresponding to G for Table 3-a givesthebearing of apparent dip, and the angle of clip.

for the new setting 01' 21.75 of core 4.

Table. 3---@ Angle Bearing of Angle of Bearing of Dip of ApparentApparent Dip. Dip Dip Degrees Curve J gives the curve corresponding tocurve J 'for' this new setting of 21.75. It will be seen that thesecurves are tangent in the region of S. 56 W. to W. Curve H. gives thebearing of the apparent dip against the angle ofapparentdipcorresponding to new setting of 24.75 and corresponds to curve H.Curve K is the corresponding curve for the new setting of 21.75corresponding tocurve K. It will be seen that the region of tangencyhere is also in the region of about S. 50 W. to W. In this region,

therefore, the apparent clips" of both core strata 12 1!. 6812 Theconclusion therefore is that the cores were taken with their axesdirected 180 away from the direction of apparent dip which was S.W.,andthe dip had an angle of 385. The lines of apparent dip weredirected in the same direction as the apparent dip at S. 65 W. and theangle of apparent dip was, for core, 24.75, and for core 4 was 21.75", adifference of 3. It will be observed that the difference between thevertical inclination of the two cores is also 3", and this would occuronly if the lines "of apparent'd'ip were directed in the same plane withthe core axes. Since, obviously, a line directed S. 65' W. is sensiblyin the same plane as a-line directed N. 67 2]., this confirms theconclusion reached by this method. The result of this orientation istherefore that the plane of the strata from which the cores-were takenwas directed S.65W. and had an inclination of 395.

The previous two examples illustrated case I, wherein thelines ofapparent dip, when positioned in the strata from which the cores aretakem'are parallel. Example 3 illustrates a case where the linesof'apparent dip are not parallel but are differently directed.

EXAMPLE 3 Core 5 was taken at a depth of 7123 feet. The bore had at thispoint a vertical inclination of 3.7.5 and a. bearingoi N. 59 W. Thiscore was traversed. in the manner previously described. The core had an.apparent dip 36. This angle was. set upon protractor i8. Scribe mark 8was placed opposite vN. 59 W. and the scribe mark H was set. opposite3.75 on protractor 9. Table 4' gives the hearing or direction of dip andthe corresponding angle. of dip, the corresponding bearingoi'. theapparent dip,v and the corresponding angle of apparent dip.

Table 4.

Angle Bearing of Angle of Bearing ofDip of Apparent Apparent Dip' DipDip Dayna Degree; 35- N. 10 W 34 33. 5 N. 47 W 32. 5 EB N170 W. 32. 533. 5 N. 87.5 32. 5 35 S. 63"W 33. 5 37' Salli W. 36 as s s. 6 W 31. 540. 5 S. 29 E. 39 40, 5 S. 71.5 39. 5 40 N. 83 E as 38. 5 N. 52 E 37. 538? 3 N. 815 34 On Fig. 9 I have charted curve M, which charts thebearing of'the dip read on the abscissa against angle of dip read on theordinate. Curve N charts the bearing of the apparent dip read on theabscissa against the angle of dip read on the ordinate. and. curve 0charts the bearing 01' the dip read'on'the abscissa against the bearingof apparent dip read on the ordinate.

Qorei was taken: at a depth oi 7183 feet. The bore at this point had avertical inclination of '2i75 and had a bearing of N. 80"- W. The scribemark I'O was set at 2.75 on protractor 9 and scribemark a'was set at N.80 W. The apparent dip of the core stratum was 39. The plane l9 was setat an angle of 39 on the protractor 18. Table '5 givesthe direction ofdip, the correspondfng'an'gle of dip, COI'I'ESDOIl'dlIlg' direction ofapordinate.

Table Angle Bearing of Angle of Bearing of Dip of Apparent Apparent DipDip Dip Degrees Degrees N. 1 E 41 N. 3 W 39. 5 N. W 39 N. 39 W 38 N. 67W 37 N. 70 W. 36- N. 88 W 36. 75 N. 79.5 W 35.75 S. 34 W- 37 S. 30 W..36 S. 71 W. 36.5 S. 7 W. S. 87 W 36.5 S. 89 W.. 35. 5 S. 25.5 E 41 S. 21E... .39. 5 S. 52.5 E 42. 5 S. 49 41 S. 79 E.. 43. 25 S. 88.5" E. 42. 5N. 58 E.. 43 S. 56 E.. 42 N. 1 E 40. 5 N. 9 W 39.5

Curve P gives the bearing of the dip read on the abscissa against angleof dip read on the ordinate. Curve Q charts the bearing of apparent dipread on the abscissa against the angle of apparent dip read on theordinate. Curve R gives the bearing of dip read on the abscissa againstthe bearing of apparent clip read on the It will be observed that curvesM and P most closely approach each other in the region of S. to S. E.,being more separated at all other bearings of the dip. The separation ofthe two curves is about 1 of angle of dip, and the two curves maytherefore be said to be sensibly tangent in this region. The conclusionwhich these curves direct is that the bearing of the dip is therefore inthe region of about S. to S. 30 to 40 E. I may select the bearing of thedip more closely. By reference to curves N, O, Q, and R, I make thefollowing series of assumptions:

Assume that the bearing of the dip is S. 10 E.. the bearing of theapparent dip of core 5, for this position of the dip is given on curve0, and its angle of dip is given on curve N. The bearing of the apparentdip of core 6 for this direction of the dip is taken from curve B, andthe angle of apparent dip is given on curve Q. If the dip is S. 10 W.,these lines of apparent dip of each core should be in this plane, andsince their direction and inclination are known, we

may, applying the theorem of descriptive geometry previously referredto, determine if the dip thus calculated equals the dip so assumed to beS. 10 E.

From the data of Tables 4 and 5 and curves of Fig. 9 when the dip is S.10 E., the angle of dip is 395. The bearing of apparent dip of core 5corresponding to a dip of S. 10 E. was S. 2 E. and its inclination was38. The bearing of the apparent dip of core 6 corresponding to a dip ofS. 10 is S. 11 E. and its inclinationwas 38.5. Assume S. as indicated atthe top of Fig. 10, with W. and E. as indicated. Draw a line UT with abearing of S. 2 E. Draw a line TV to make an angle UTV equal to 38. Drawa line TW with a bearing of S. 11 E. Draw a line XT so that the angleXTW equals 38.5. Draw a line UV perpendicular to line TU. Draw a line XWequal in length to UV and perpendicular to 'IW. Draw a line ZZ' throughthe points W and U as the strike of the plane defined by the lines ofapparent dip. Draw the line TT' perpendicular to the line 22'. Line TTis the bearing of the dip of the plane and its bearing is S. 7 E. Layoff the line T'Y equal to the line UV. Draw the line TY. The angle T'Tyis the angle of dip of the dip TT. This angle is 385. This constructiongives the dip as 385 S. 7 E. The assumed dip from the curves of Fig. 9is 395 S. 10 E. The difierence is 3 in bearing and 1.5 in in clination.

Assume the di as 39 S. The bearing-of the core 6 is S. 3 E. and itsinclination is 38.

'apparent dip of core 5 is S. 10 W. and its inclinasponding bearing ofthe apparent dip of core 6 is S. 5 W. and its inclination is 38'. Thedip was determined by construction according to the above method to beS. 2 W. and its inclination was determined to be 38. This compares withthe assumed dip 39.5 S. 10 W. This indicates a difference of 8 inbearing. The closest agreement therefore between the dip as determinedby the curves for the position of parallelism of the simulated dips ofcores 5 and 6 and the dip of the plane defined by the lines of apparentdip is that for a position of S. 10 W. where the agreement is within 3"."I therefore determine the dip of the strata from which cores 5 and 6were taken as having a dip of about 39.5 in inclination with a bearingof about S. 10 E.

It will be seen that whereas a vertical core. i. e., one not having anydirection or inclination. may be employed in this method, as in thecases illustrated by Examples 1 and 2, it may notbe employed in the caseillustrated by Example 3. In that case the traverse of a vertical corewill give a straight line on Fig. 9 at an angle of dipof 39.5", and thisline will intersect curves M or P at two points, giving an indeterminateanswer for the dip. However, if two differently deviated cores, such ascores 5 and 6, are employed, an

additional vertical core taken from the same stratum will intersect thecurves of the traverse of both cores at their region of tangency, andthus further confirm the results obtained.

The instrument herein described may also be employed for correction ofthe readings obtained by the socalled magnetic method of coreorientation. In that method but a single core is required. The core issurveyed by a magnetomtor.

eter or other exploring magnet and the magnetic north pole of the coreis determined. Since the position of the line of apparent dip withrespect to the north pole is fixed, and knowing the magnetic declinationat the point where the location of the cores north pole is determined,the bearing of the line of apparent dip is thus established. Since,however, if the core is not a vertical core but has a verticalinclination or an azimuthal deviation when taken in the stratum,acorrection for such deviation must be made in order to get the true dipof the core stratum.

My instrument permits of this correction. I proceed in the followingmanner. With spindle II vertical and base Ia level, set the angle onprotractor 18 to the angle of apparent dip of the core stratum. Rotatearm I! until rod 22, when brought level, is so directed that aperpendicularto the projection of rod 22 on base la has the bearing asdetermined for the line of apparent dip by means of the magneticorienta- Tighten the set screws l3 and I6. Set the scribe marks 8 and I0 at the bearing and inclination of the core axis as determined by thewell survey, i. e., that of the bore from which the core is taken. Readthe bearing of the dip by setting the rod 22 level and determining thebearingoi Thus, for example, a core has-a core stratum 3'10! apparentdip of iand-an axis which when 1 the core was taken vhad averticalinclination zof'20 and a bearing N. .30 W. .Theabearing of theline of apparent-dip with the core vertical is determined by themagnetic method to be S. 26.5 W. Set spindle H vertical. ;Set 30 onprotractor I 8. Set'therod 522 level, and rotate irod 11 so that aperpendicular .to the projection :nf 22-0n base la has atbearing ofS..-281W. Set the set screws. Set the scribe mark 8-at N. 30 W. EBet'the scribe mark 10 -at .20. 22 and read thebearing of the dip aspreviously described. 'It is S.-8 W. Read-the-angleof dip on protractor25. It is .43. The-true dip is then -.43 S.8 W.

Where in the claims reference is made tocore :strata and to core axisand toprocedural steps involving the same, they .include the simulated-,corestrata.and the simulatedvcore .axis as set up -on the apparatusherein described .and to procedural steps therewith.

.It is to be understood that .the foregoing de- .scription of myinvention is illustrative only, and various changes and modificationsmay be .made therein coming within the scope of the appended claims.

I claim:

1. Amethod ;for determining the dip of strata, which comprises takingaplurality of differently .deviated cores from the same -or substantiallyparallel strata, determining'the inclination and direction of the axesof such cores as taken,establishing the apparent angle of (lip of thecore strata in each of said cores, establishing the axes of said coresin space in the said direction and at the 'said inclination, determiningthe angle of dip of said core strata ,for various bear- 'ings of the dipof the 'core'stratawhen'said core strata are rotated about the axis 'oftheir respective cores when so directed and inclined, establishingthebearing and angle of dip of each of said core strata at which saidangleand bearing of dip of each of said core strata are equal, and thusdetermining the bearing "and angle of :dlpof the strata from'which'thecoresare taken.

2. A method for determining the dip-of strata, which comprises taking aplurality of differently deviated cores from the same or substantiallyparallel strata, determining the inclination and direction of the axesof such cores as taken, establishing the apparent angle of 'dip'of thecore strata in each of said cores, establishing the axes of said coresin space in the said direction and at the said inclination, determiningthe angle and bearing of the apparent dip of said core 'strata forvarious bearings of the dip of the core strata when rotated about "theaxis oftheir re- .spective cores when so inclined-and directed, de-*termining also the angle of dip of said core'strata "and the bearing ofthe dip 'of saidqcore-strata'for :each of the said determineddirections-of the apparent dip of said cores, and from saiddeterminations establishing the angle of dip and the Pbearingof thedipofsaid strata from which-said cores are taken.

'3. .A method for determining the ;'dip :of strata,

V which comprises taking aplurality of difierently deviated cores fromthe same or substantially parallel strata, determining the-inclinationand direction of the axes of such cores as taken,

. :"establishing the apparent angle :of dip .of the w Level the :rod

16 strata in each of said cores, establishing the axes of said cores inspace in the said direction and at the said inclination, determining theangle of dip of said core strata for various bearings of the dip ofthe-core stratawhen said core strata are rotated about the axis of theirrespective cores when so directed and inclined, and from saiddetermination establishing a plurality of curves relating the angle ofdip of each of said core strata determined for each of said variousdirections of dip to the bearing of the dip, and

determining the .direction and angle of dip of said strata from whichsaid cores are taken as that direction and angle of dip at which thecurves are at their closest approach.

4..A.method for determining the dip of strata, which comprises taking aplurality-of differently deviated cores from the same or substantially.parallel strata, determining the inclination and .direction of the axesof said-cores as taken, es-

tablishing the apparent angle of dip of the core strata in each :of saidcores, determining the angle of dip-of said core strata for variousbear- 'illgs'of the dip :of the core strata when rotated :aboutthe-axis-of their respective cores 'When'sald axes are inclined anddirectedwin-accordance with ,said determinationsof the inclination anddirection of the cores in the formations from which they aretaken,determining the angle and bearing of the apparent dip of said corestrata for said various bearings of-the dip of thecore strata when sorotated about the axes of their respective cores so inclined anddirected, and from v said determination establishing -a plurality ofcurves relating the bearings of the dip of each :of said core strata asdetermined for each of said various bearings of the dip, establishing aplurality of curves relating the angle of apparent dip to the variousbearings 'of the apparent dip, establishing the angle :and bearing oithe-dip of -said strata from which the cores are taken asthat-determined by the closest'approach of the curves relatingthe angleof dip *to the bearingof the dip, and confirming said dip so determined.by {establishing that the corresponding angles andbearings-of theapparent dip determined for :said bearing of the dipjandangle of di liesubstantially in the .plane whose -dip has a bearing and inclination asdetermined.

5. Amethod for determining the'dip of strata,

' 'which comprises taking a iplurality of differently they are taken,determining the angle and bearing of the apparent 'dip of saidwcorestrata for :said various bearings of the-dip ofthe core strata whensorotatedabout the axes of their respective cores so inclined anddirected, and from said -d'etermination establishing a plurality ofcurves relating the bearings of "the dip of each of said corestrata'asdetermined'ior each of said various "bearings of the dip, establishing aplurality of curves relating the angle of apparentdip to the variousbearings of the apparent dip and. a

';plurality of curves relating the bearing of appar-- ent dip to 'thebearing of the '"dip for various bearings of saiddip, establishing theangle and bearing of the dip of said strata from which the cores aretaken as that determined by the closest approach of the curves relatingthe angle of dip to the bearing of the dip, and confirming said clip sodetermined by establishing that the corresponding angles and bearings ofthe apparent dip determined for said bearing of the dip and angle of diplie substantially in the plane whose clip has a bearing and inclinationas determined.

6. An apparatus for the determination of dip of strata, which comprisesa base, a rod mounted on said base, means for fixing said rod at adesired bearing and at a desired inclination to the vertical to saidbase, a plane, means for mounting said plane on said rod, means foradjusting said plane to the desired inclination to said rod, means forrotating said plane around said rod, a second rod mounted on said plane,means for positioningsaid rod on said plane parallel to said base, athird rod mounted on said second rod and perpendicular thereto, meansfor determining the inclination of said third rod to the base, means fordetermining the direction or bearing of said third rod comprising aprotractor swivelly mounted on said third rod, and means for levellingthe edge of said protractor.

'7. An apparatus for the determination of dip of strata, which comprisesa base, a rod mounted on said base, means for fiXil'ig said rod at adesired bearing and at a desired inclination to the vertical to saidbase, a plane, means for mounting said plane on said rod, means foradjusting said plane to the desired inclination to said rod, means forrotating said plane around said rod, a second rod mounted on said plane,means for positioning said rod on said plane parallel to said base, athird rod mounted on said second rod and perpendicular thereto, meansfor determining the inclination of said third rod to the base comprisinga protractor swivelly mounted on said third rod and means for levellingthe edge of said protractor, means for determining the direction orbearing of said third rod, a hinge, means for mounting said hingeparallel to said plane and at an angle to said first-named rod equal tothat at which said plane is set, a protractor swivelly mounted on saidhinge, and means for levelling the edge of said protractor.

8. A method for determining the dip of strata from which a plurality ofdifferently deviated cores have been taken from the same orsubstantially parallel strata and for which the in-- clination anddirection of the axes of such cores are known, which comprisesestablishing the apparent angle of dip of the core strata in each ofsaid cores, establishing the axes of said cores in space in the saiddirection and at the said inclination, determining the angle of dip ofsaid core strata for various bearings of the dip of the core strata whensaid core strata are rotated about the axis of their respective coreswhen so directed and inclined, establishing the bearing and angle of dipof each of said core strata at which said angle and bearing of dip ofeach of said core strata are equal, and thus determining the bearing andangle of dip of the strata from which the cores are taken.

9. A method for determining the dip of strata from which a plurality ofdiiierently deviated cores have been taken from the same or substantiallparal1e1 strata and for which the inclination and direction of the axesof such cores are known, which comprises establishing the apparent angleof dip of the core strata in each of said cores, establishing the axesof said cores in space in the said direction and at the saidinclination, determining the angle and bearing of the apparent dip ofsaid core strata for various bearings of the dip of the core strata whenrotated about the axis of their respective cores when so inclined anddirected, determining also the angle of dip of said core strata and thebearing of the dip of said core strata for each of the said determineddirections of the apparent dip of said cores, and from saiddeterminations establishing the angle of dip and the bearing of the dipof said strata from which said cores are taken.

10. A method for determining the dip of strata from which a plurality ofdifferently deviated cores have been taken from the same orsubstantially parallel strata and for which the inclination anddirection of the axes of such cores are known, which comprisesestablishing the apparent angle of dip of the core strata in each ofsaid cores, establishing the axes of said cores in space in the saiddirection and'at the said inclination, determining the angle of dip ofsaid core strata for various bearings of the dip of the core strata whensaid core strata are rotated about the axis of their respective coreswhen so directed and inclined, and from said determination establishinga plurality of curves relatin the angle of dip of each of said corestrata determined for each of said various directions of dip to thebearing of the dip, and determining the direction and angle of dip ofsaid strata from which said cores are taken as that direction and angleof dip at which the curves are at their closest approach.

11'. A method for determining the dip of strata from which a pluralityof differently deviated cores have been taken from the same orsubstantially parallel strata and for which the inclination anddirection of the axes of said cores are known, which comprisesestablishing the apparent angle of dip of the core strata in each ofsaid cores, determining the angle of dip of said core strata for variousbearings of the dip of the core strata when rotated about the axis oftheir respective cores when said axes are inclined and directed inaccordance with said determinations of the inclination and direction ofthe cores in the formations from which they are taken, determining theangle and bearing of the apparent dip of said cores strata for saidvarious bearings of the dip of the core strata when so rotated about theaxes of their respective cores so inclined and directed, and from saiddetermination establishing a plurality of curves relatin the bearings ofthe dip of each of said core strata as determined for each of saidvarious bearings of the dip, establishing a plurality of curves relatingthe angle of apparent dip to the various bearings of the apparent dip,establishing the angle and bearing of the dip of said strata from whichthe cores are taken as that determined by the closest approach of thecurves relating the angle of dip to the bearing of the dip, andconfirming said dip so determined by establishing that the correspondingangles and bearings of the apparent dip determined for said bearing ofthe dip and angle of dip lie substantially in the plane whose dip has abearing and inclination as determined.

12. A method for determining the dip of strata from which a plurality ofdifierently deviated cores have been taken from the same orsubstantially parallel strata and for which the inclination anddirection of the axes of said cores are known, which comprisesestablishing the apparent angle of dip'of the core strata in each ofsaid cores, determining the angle of dip of said core strata for variousbearings of the dip of the core strata when rotated about the axis oftheir respective cores when said axes are inclined and directed inaccordance with said determinations of the inclination and direction ofthe cores in the formations from which they are taken, determining theangle and bearing of the apparent dip of said core strata for saidvarious bearings of the dip of the core strata when so rotated about theaxes of their respective cores so inclined and directed, and from saiddetermination establishing a plurality of curves relating the bearingsof the dip of each of said core strata as determined for each of saidvarious bearings of the dip, establishing a plurality of curves relatingthe angle of apparent dip to the various bearings of the apparent dipand a plurality of curves relating the bearing of apparent dip to thebearing of the dip for various bearings of said dip, establishing theangle and bear- REFERENCES CITED The following references are of recordin the file of this patent:

UNITED STATES PATENTS Number Name Date 1,921,508 Dawson Aug. 8, 19332,089,216 Lynton Aug. 10, 1937 2,149,715 Pearson Mar. 7, 1939 2,149,716Beattie Mar. '7, 1939 2,183,765 Coleman Dec. 19, 1939

